Non-Gaussian Concentration Profile of Hydrogen Diffused in the Zinc Oxide Bulk Crystal

Abstract

Hydrogen in ZnO is characteristic for its by high mobility and limited solubility; consequently, the classical Gaussian broadening expected for diffusion from a localized source is not observed after post-implantation annealing. In this work, c-axis ZnO single crystals were implanted with 1 MeV H⁺ (fluence 1 x 10¹⁶ cm^-2), annealed in flowing O₂ at 300°C and 600°C for 15–30 min, and their depth profiles were quantified by secondary ion mass spectrometry. The profiles were observed to evolve in a non-Gaussian manner. At 300°C the peak narrows and increases, whereas at 600°C the near-peak region is depleted. A long, asymmetric tail and a surface-proximal excess are developed, indicating that rapid out-diffusion, trapping, and limited solubility govern the evolution rather than Fickian spreading. The diffusion coefficient D at 600°C was extracted directly from the difference between the initial and annealed profiles. A semi-infinite model with an absorbing surface, with no need to assume a Gaussian initial profile, was applied. Reduction in the overall content after 15 and 30 min at 600°C yields the value of D = 6 x 10^-9 cm²/s. These results provide a consistent framework for extracting diffusion parameters from non-Gaussian profiles in hydrogenated ZnO, highlighting the dominant role of surface exchange, trapping, and low equilibrium solubility in shaping the measured hydrogen distributions.